A blocked pipe is inconvenient and can result in a mess, but it is usually quickly fixable. Hair and soap scum can form a clog that prevents water from flowing through the pipe properly. The clog becomes self-perpetuating as it grows because it prevents other debris from passing, and that debris joins the clog as well. Caustic soda, used as a drain cleaner, is a highly corrosive material that often breaks up pipe clogs. If the soda didn't work or is solidified, you need to try alternative methods.
Pour a bucket of hot water down the drain so it reaches the blocked pipe. The water, heat and pressure should help break up the solidified caustic soda.
Insert a power drain snake into the drain or pipe and twist it when you feel it hit a blockage. This helps lodge the snake into the clog. Some power snakes operate with a foot pedal, where you push down on the pedal to release the cable so you can feed it down the pipe with your hands.
Turn on the snake so it vibrates and move it back and forth through the pipe. This helps eliminate the clog while breaking up any remaining solid deposits. Be careful when pulling the snake back to prevent caustic soda from splashing as the snake exits the drain. If your power snake has an auto-feeder, change the direction and use the pedal to pull the snake back in from the pipe when you're done.